A digital radio communication system uses a modulation system such as phase shift keying (PSK) or quadrature amplitude modulation (QAM) in order to improve frequency use and transmission characteristics.
In the PSK or QAM modulation system, information is loaded on a phase for modulation. Accordingly, when there is a carrier frequency offset due to a frequency offset in transmitters at a transmitting side and a receiving side, transmission characteristics are greatly degraded by phase rotation due to the carrier frequency offset.
In order to avoid the degradation of the transmission characteristics due to the carrier frequency offset, the PSK or QAM modulation system requires estimating the carrier frequency offset and correcting the offset in the transmitter using any means.
Methods of estimating a carrier frequency offset includes a method of estimating a carrier frequency offset using a previously determined sequence of training signals, and a blind method not requiring training signals.
The blind method can realize high transmission efficiency since the training signals are unnecessary. However, the carrier frequency offset cannot be estimated in a short time.
Accordingly, a radio communication system that performs burst transmission in which the carrier frequency offset is required to be estimated in a short time uses the method of estimating a carrier frequency offset using a previously determined sequence of training signals (Non-patent Document 1).
FIG. 15 is a diagram showing a transmission device 5 and a reception device 6 in a radio communication system 300. The radio communication system 300 using a method of estimating a carrier frequency offset using a known sequence of training signals shown in Non-patent Document 1 will be described with reference to FIG. 15. The radio communication system 300 includes the transmission device 5 and the reception device 6.
The transmission device 5 includes a training signal sequence generation unit 51, a radio unit 52, and a transmitting antenna 53.
The training signal sequence generation unit 51 generates a previously determined sequence of training signals.
The radio unit 52 performs analog conversion and frequency conversion on the training signals generated by the training signal sequence generation unit 51, and transmits a radio signal from the transmitting antenna 53 to the reception device 6.
The reception device 6 includes a receiving antenna 61, a radio unit 62, a phase difference detection unit 63, an averaging unit 64, and a frequency estimation unit 65.
The receiving antenna 61 receives the radio signal transmitted from the transmission device 5.
The radio unit 62 performs frequency conversion and digital conversion on the radio signal received by the receiving antenna 61 to generate a reception signal.
The phase difference detection unit 63 compares the reception signal with training signals that are based on a previously determined sequence, and detects physical amounts including effects of noise obtained depending on phase shift amounts for a period of time. In Non-patent Document 1, the training signals are a sequence of signals repeated at intervals of 0.8 μs, and the reception signal is delayed 0.8 μs to detect the physical amounts that are a function of phase shift amounts for 0.8 μs.
The averaging unit 64 averages the physical amounts detected by the phase difference detection unit 63 in order to avoid the effects of the noise.
The frequency estimation unit 65 estimates a carrier frequency offset from the averaged physical amount obtained by the averaging unit 64.
Next, an operational principle of a conventional method of estimating a carrier frequency offset will be described using formulas.
Symbol n denotes a sample number, and symbol s(n) denotes the training signal generated by the training signal sequence generation unit 51. A reception signal y(n) obtained through the reception in the receiving antenna 61, the frequency conversion in the radio unit 62, and the digital conversion in the radio unit 62 is expressed by Formula 1.
                    [                  Formula          ⁢                                          ⁢          1                ]                                                                      y          ⁡                      (            n            )                          =                                            s              ⁡                              (                n                )                                      ·                          exp              ⁡                              (                                                      j                    ·                    2                                    ⁢                                      π                    ·                                                                  Δ                        ⁢                                                                                                  ⁢                        f                                                                    f                        s                                                              ·                    n                                                  )                                      ·            h                    +                      η            ⁡                          (              n              )                                                          (        1        )            
Here, symbol h denotes a complex amplitude response between the transmitting antenna 53 and the receiving antenna 61. Symbol Δf denotes a carrier frequency offset between the transmission device 5 and the reception device 6. Symbol fs denotes a sampling frequency. Symbol η(n) is a noise independent for each sample and dependent on a complex Gaussian distribution in which an average power amount is 1.
For simplification of explanation, it is assumed hereinafter that an absolute value (|s(n)|) of the training signal s(n) for each sample is 1.
The phase difference detection unit 63, the averaging unit 64, and the frequency estimation unit 65 estimate a carrier frequency offset Δf using the reception signal y(n) generated from the received radio signal and the training signal s(n) generated by the training signal sequence generation unit 51.
The training signal s(n) is a training signal that is based on a previously determined signal sequence.
When the phase difference detection unit 63 uses delay-detection-type phase difference detection, that is, when a conjugate complex number of a delay detection result in a time difference τ sample of the reception signal y(n) is multiplied by a conjugate complex number of a delay detection result in a time difference τ sample of the training signal s(n), a physical amount z(n) that is a function of phase shift amounts in the time difference τ sample is expressed by Formula 2.
                    [                  Formula          ⁢                                                            ⁢                                                          ⁢          2                ]                                                                                                                z                ⁡                                  (                  n                  )                                            =                            ⁢                                                                    s                    *                                    ⁡                                      (                    n                    )                                                  ·                                  s                  ⁡                                      (                                          n                      -                      τ                                        )                                                  ·                                  y                  ⁡                                      (                    n                    )                                                  ·                                                      y                    *                                    ⁡                                      (                                          n                      -                      τ                                        )                                                                                                                          =                            ⁢                                                                    exp                    ⁡                                          (                                                                        j                          ·                          2                                                ⁢                                                  π                          ·                                                                                    Δ                              ⁢                                                                                                                          ⁢                              f                                                                                      f                              s                                                                                ·                          τ                                                                    )                                                        ·                  h                  ·                                      h                    *                                                  +                                                                                                      ⁢                                                h                  ·                                      s                    ⁡                                          (                                              n                        -                        τ                                            )                                                        ·                                      exp                    ⁡                                          (                                                                        j                          ·                          2                                                ⁢                                                  π                          ·                                                                                    Δ                              ⁢                                                                                                                          ⁢                              f                                                                                      f                              s                                                                                ·                          n                                                                    )                                                        ·                                                            η                      *                                        ⁡                                          (                                              n                        -                        τ                                            )                                                                      +                                                                                                      ⁢                                                                    h                    *                                    ·                                                            s                      *                                        ⁡                                          (                      n                      )                                                        ·                                      exp                    ⁡                                          (                                                                                                    -                            j                                                    ·                          2                                                ⁢                                                  π                          ·                                                                                    Δ                              ⁢                                                                                                                          ⁢                              f                                                                                      f                              s                                                                                ·                                                      (                                                          n                              -                              τ                                                        )                                                                                              )                                                        ·                                      η                    ⁡                                          (                      n                      )                                                                      +                                                                                                      ⁢                                                                    s                    *                                    ⁡                                      (                    n                    )                                                  ·                                  s                  ⁡                                      (                                          n                      -                      τ                                        )                                                  ·                                  η                  ⁡                                      (                    n                    )                                                  ·                                                      η                    *                                    ⁡                                      (                                          n                      -                      τ                                        )                                                                                                                          =                            ⁢                                                                    exp                    ⁡                                          (                                                                        j                          ·                          2                                                ⁢                                                  π                          ·                                                                                    Δ                              ⁢                                                                                                                          ⁢                              f                                                                                      f                              s                                                                                ·                          n                                                                    )                                                        ·                                      {                                                                                                                      h                                                                          2                                            +                                              h                        ·                                                  α                          ⁡                                                      (                                                          n                              -                              τ                                                        )                                                                                              +                                                                        h                          *                                                ·                                                                              α                            *                                                    ⁡                                                      (                            n                            )                                                                                                                }                                                  +                                                                                                      ⁢                                                                    s                    *                                    ⁡                                      (                    n                    )                                                  ·                                  s                  ⁡                                      (                                          n                      -                      τ                                        )                                                  ·                                  η                  ⁡                                      (                    n                    )                                                  ·                                                      η                    *                                    ⁡                                      (                                          n                      -                      τ                                        )                                                                                                          (        2        )            
In Formula 2, α(n) is expressed by Formula 3.
                    [                  Formula          ⁢                                          ⁢          3                ]                                                                      α          ⁡                      (            n            )                          =                              s            ⁡                          (              n              )                                ·                      exp            ⁡                          (                                                j                  ·                  2                                ⁢                                  π                  ·                                                            Δ                      ⁢                                                                                          ⁢                      f                                                              f                      s                                                        ·                  n                                            )                                ·                                    η              *                        ⁡                          (              n              )                                                          (        3        )            
When the averaging unit 64 averages physical amounts z(n) of N samples, an averaged physical amount φ is expressed by Formula 4 if the sample number N is greater than a value of the time difference τ sample (phase difference N>τ).
                    [                  Formula          ⁢                                          ⁢          4                ]                                                                                                Φ              =                            ⁢                                                ∑                                      n                    =                    1                                    N                                ⁢                                  z                  ⁡                                      (                    n                    )                                                                                                                          =                            ⁢                                                exp                  ⁡                                      (                                                                  j                        ·                        2                                            ⁢                                              π                        ·                                                                              Δ                            ⁢                                                                                                                  ⁢                            f                                                                                f                            s                                                                          ·                        τ                                                              )                                                  ·                                  {                                                            N                      ·                                                                                                  h                                                                          2                                                              +                                                                  ∑                                                  n                          =                                                      1                            -                            τ                                                                          0                                            ⁢                                                                        h                          ·                          α                                                ⁢                                                  (                          n                          )                                                                                      +                                                                                                                                                          ⁢                                                      2                    ·                                                                  ∑                                                  n                          =                          0                                                                          N                          -                          τ                                                                    ⁢                                              Re                        [                                                  h                          ·                                                      α                            (                            n                            )                                                                          ]                                                                              +                                                            ∑                                              n                        =                                                  N                          -                          τ                          +                          1                                                                    N                                        ⁢                                                                  h                        *                                            ·                                                                        α                          *                                                ⁡                                                  (                          n                          )                                                                                                                    }                            +                                                                                        ⁢                                                ∑                                      n                    =                    1                                    N                                ⁢                                                                            s                      *                                        ⁡                                          (                      n                      )                                                        ·                                      s                    ⁡                                          (                                              n                        -                        τ                                            )                                                        ·                                      η                    ⁡                                          (                      n                      )                                                        ·                                                            η                      *                                        ⁡                                          (                                              n                        -                        τ                                            )                                                                                                                              (        4        )            
In Formula 4, symbol Re[•] denotes a real number.
When the sample number N is equal to or smaller than the value of the time difference τ sample (phase difference N≦τ), the averaged physical amount φ is expressed by Formula 5.
                    [                  Formula          ⁢                                          ⁢          5                ]                                                                                                Φ              =                            ⁢                                                ∑                                      n                    =                    1                                    N                                ⁢                                  z                  ⁡                                      (                    n                    )                                                                                                                          =                            ⁢                                                exp                  ⁡                                      (                                                                  j                        ·                        2                                            ⁢                                              π                        ·                                                                              Δ                            ⁢                                                                                                                  ⁢                            f                                                                                f                            s                                                                          ·                        τ                                                              )                                                  ·                                  {                                                            N                      ·                                                                                                  h                                                                          2                                                              +                                                                  ∑                                                  n                          =                                                      1                            -                            τ                                                                                                    N                          -                          τ                                                                    ⁢                                                                        h                          ·                          α                                                ⁢                                                  (                          n                          )                                                                                      +                                                                                                                                                          ⁢                                                      ∑                                          n                      =                      1                                        N                                    ⁢                                                            h                      *                                        ·                                                                  α                        *                                            (                      n                      )                                                                      }                            +                                                                                        ⁢                                                ∑                                      n                    =                    0                                    N                                ⁢                                                                            s                      *                                        ⁡                                          (                      n                      )                                                        ·                                      s                    ⁡                                          (                                              n                        -                        τ                                            )                                                        ·                                      η                    ⁡                                          (                      n                      )                                                        ·                                                            η                      *                                        ⁡                                          (                                              n                        -                        τ                                            )                                                                                                                              (        5        )            
When the phase difference detection unit 63 uses the delay detection, the frequency estimation unit 65 calculates an estimate fest of the carrier frequency offset, based on Formula 6.
                    [                  Formula          ⁢                                          ⁢          6                ]                                                                      f          est                =                                            f              s                                      2              ⁢                              π                ·                τ                                              ·                                    tan                              -                1                                      ⁡                          (                                                Im                  ⁡                                      [                    Φ                    ]                                                                    Re                  ⁡                                      [                    Φ                    ]                                                              )                                                          (        6        )            
In Formula 6, symbol Im[•] denotes an imaginary number.
When the effects of the noise η(n) in the averaged physical amount φ are negligibly smaller, components other than a first term included in brackets { } in Formula 4 or 5 are 0 (zero), that is, Formula 4 or 5 includes only a real number component. Accordingly, the estimate fest of the carrier frequency offset can be calculated without an error.
However, effects of the noise η(n) cannot be neglected in a general radio communication system. Error estimation when the effects of the noise η(n) cannot be neglected will now be described using formulas.
The noise η(n) is independent for each sample and stochastically dependent on a complex Gaussian distribution. Accordingly, when two independent variables dependent on the Gaussian distribution are subjected to a linear operation, an averaged physical amount Φ of N>τ in Formula 4 may be expressed as Formula 7 by the nature of the Gaussian distribution. The nature of the Gaussian distribution includes a nature of approximation to a Gaussian distribution with a variance obtained through a linear operation of variances of two variables.
When two independent variables dependent on the Gaussian distribution are multiplied, a distribution that is not strictly a Gaussian distribution, but that is close to a Gaussian distribution is obtained. Accordingly, it is assumed hereinafter that the distribution can be approximated to a Gaussian distribution with a variance obtained by multiplying the variances of the two variables.
                                              ⁢                  [                      Formula            ⁢                                                  ⁢            7                    ]                                                                    Φ        =                              exp            ⁡                          (                                                j                  ·                  2                                ⁢                                  π                  ·                                                            Δ                      ⁢                                                                                          ⁢                      f                                                              f                      s                                                        ·                  τ                                            )                                ·                      {                                          N                ·                                                                          h                                                        2                                            +                                                                                                                  (                                                                              2                            ⁢                            N                                                    -                          τ                                                )                                            ·                                                                                                  h                                                                          2                                                              +                                          N                      2                                                                      ·                                  η                  r                                            +                              j                ·                                                                            τ                      ·                                                                                                  h                                                                          2                                                              +                                          N                      2                                                                      ·                                  η                  i                                                      }                                              (        7        )            
The averaged physical amount φ when N≦τ in Formula 5 may be expressed as Formula 8.
                                              ⁢                  [                      Formula            ⁢                                                  ⁢            8                    ]                                                                    Φ        =                              exp            ⁡                          (                                                j                  ·                  2                                ⁢                                  π                  ·                                                            Δ                      ⁢                                                                                          ⁢                      f                                                              f                      s                                                        ·                  τ                                            )                                ·                      {                                          N                ·                                                                          h                                                        2                                            +                                                                                          N                      ·                                                                                                  h                                                                          2                                                              +                                          N                      2                                                                      ·                                  η                  r                                            +                              j                ·                                                                            N                      ·                                                                                                  h                                                                          2                                                              +                                          N                      2                                                                      ·                                  η                  i                                                      }                                              (        8        )            
In Formulas 7 and 8, the noises ηr and ηi are variables dependent on the Gaussian distribution in which the variance is 1.
Here, the case where a total power of reception signals used for estimation of the carrier frequency offset is sufficiently higher than noise power, that is, the case expressed by Formula 9 will be described.[Formula 9]N·|h|2>>1  (9)
When the total power is expressed by Formula 9, the estimate fest of the carrier frequency offset calculated by the frequency estimation unit 65 uses a relationship of tan θ is nearly equal to θ when θ takes a sufficiently smaller value than 1 (θ<<1). When N>τ, the estimate fest of the carrier frequency offset is approximated by Formula 10.
                    [                  Formula          ⁢                                          ⁢          10                ]                                                                      f          est                ≈                              Δ            ⁢                                                  ⁢            f                    +                                                    f                s                                            2                ⁢                                  π                  ·                                                            τ                      ·                      N                      ·                                                                                                  h                                                                          2                                                                                                                  ⁢                                                                                1                    N                                    +                                      1                                          2                      ⁢                                              τ                        ·                                                                                                          h                                                                                2                                                                                                                                ·                              η                θ                                                                        (        10        )            
When N≦τ, the estimate fest, of the carrier frequency offset is approximated to Formula 11.
                    [                  Formula          ⁢                                          ⁢          11                ]                                                                      f          est                ≈                              Δ            ⁢                                                  ⁢            f                    +                                                    f                s                                            2                ⁢                                  π                  ·                  τ                  ·                                                          h                                                        ·                                      N                                                                        ⁢                                                            1                  +                                      1                                          2                      ⁢                                                                                                  h                                                                          2                                                                                                        ·                              η                θ                                                                        (        11        )            
In Formulas 10 and 11, the noise ηθ is a variable dependent on the Gaussian distribution in which the variance is 1.
An acquisition range in which the carrier frequency offset can be estimated is defined, for example, by Formula 12.
                    [                  Formula          ⁢                                          ⁢          12                ]                                                                      -                                    f              s                                      2              ⁢              τ                                      <                  f          est                <                              f            s                                2            ⁢            τ                                              (        12        )            
As shown in Formula 10 or 11, a conventional carrier frequency offset estimation system can reduce an estimation error of the carrier frequency offset as a sampling rate is lower, a time of the time difference τ sample is longer, a reception level |h|2 is higher, and an averaging sample number N is greater. Among them, a range in which the sampling rate fs and the time difference τ sample can be set are limited by the acquisition range of the carrier frequency offset shown in Formula 12.
Accordingly, the conventional frequency offset estimation system determines a sampling rate fs and the value of a time difference τ sample from the acquisition range of required carrier frequency offsets. The system then determines the sample number N from an allowed estimation error and an assumed reception level |h|2.
However, in a multi-path environment such as non-line-of-sight propagation, a plurality of paths are added in a reverse phase and the reception level is greatly degraded with a certain probability. For example, in a Rayleigh fading environment, the probability that an instantaneous reception level will be at least 20 dB lower than an average reception level is about 1%. This Rayleigh fading environment is a general model of a multi-path environment.
Accordingly, when a conventional carrier frequency offset estimation system is used in a multi-path fading environment, it is necessary to set an averaging sample number to a value sufficiently greater than the number defined as a carrier-to-noise ratio (CNR) and to sufficiently increase an average reception level in order to prevent an estimation error from increasing due to reception level degradation. This causes degradation of frame use efficiency, an increase of a carrier frequency offset estimation time, and an increase of consumption power and cost of a transmission device due to increased transmission power, as a long training signal is assigned.
[Non-patent Document 1] Masahiro Morikura, Shuji Kubota, et al., “Revised version 802.11 High-speed Wireless LAN Textbook”, Impress, pp. 204-205, 2005